BMS201 Engineering Statistics Tutorial 5 1.Use the standard normal table to find the following: a) P( Z 1.75) b) P( Z 1.32) c) P(1.6 Z 2.37) d) P( Z 1.29) e) P( Z 4.5) f) P( Z 4.5) [0.9599,0.9066,0.9363,.9015,0,0] 2.Given a standard normal distribution, find the value of k such that a) P( Z k ) 0.0427 b) P( Z k ) 0.2946 c) P(0.93 Z k ) 0.7235. [-1.72,0.54,1.28] 3.The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter. a) What proportion of rings will have inside diameters exceeding 10.075 centimeters? b) What is the probability that a piston ring will have an inside diameter between 9.97 and 10.03 centimeters? c) Below what value of inside diameter will 15% of the piston ring fall? [0.0062, 0.6826, 9.969] 4.If a set of observations are normally distributed, what percent of these differ from the mean by a) more than 1.3 ? b) less than 0.52 ? [19.36%,39.70%] 5.A soft drink machine is regulated so that it discharges an average of 200ml per cup. If the amount of drink is normally distributed with a standard deviation equal to 15ml, a) What fraction of cups will contain more than 224ml? b) What is the probability that a cup contains between 191ml and 209ml? c) How many cups will probably overflow if 230ml cup are used for next 1000 drinks? d) Below what value do we get the smallest 25% of the drink? [0.0548,0.4514,23,189.95ml] 6.The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis regardless of their other qualifications? [29] 174 7. Masses of a particular article are normally distributed with mean 20g and standard deviation 2g. If a sample of 12 such article is chosen, find the probability that the total mass is less than 230g. (pg 422) [0.0749] 8.The maximum load a lift can carry is 450kg. The weights of men are normally distributed with mean 60kg and standard deviation 10kg. The weights of women are normally distributed with mean 55kg and standard deviation 5kg. Find the probability that the lift will be overloaded by 5 men and 2 women, if their weight are independent. (pg 433) [0.0436] 9.The weight of a large loaf of bread is a normal variable with mean 420g and standard deviation 30g. The weight of a small loaf of bread is a normal distribution with mean 220g and standard deviation 10g. a) Find the probability that 5 large loaves weigh more than 10 small loaves. b) Find the probability that the total weight of 5 large loaves and 10 small loaves lies between 4.25kg and 4.4kg. [0.0885,0.6601] 10.A coin is tossed 400 times. Find the probability of obtaining a) between 185 and 210 heads inclusive; b) exactly 205 head; c) less than 176 or more than 227 heads. [0.7925,0.0352,0.0101] 11.A pair of dice is rolled 180 times. What is the probability that a total of 7 occurs a) at least 25 times? b) between 33 and 41 inclusive? c) exactly 30 times? [0.8643,0.2978,0.0796] 175

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